LED: LED.fr

File LED.fr, 20.7 KB (added by claudeduhr, 7 years ago)

The model file for LED

Line 
1(***************************************************************************************************************)
2(******               This is the FeynRules mod-file for the Large Extra Dimensions                       ******)
3(******                                                                                                   ******)
4(******     Author: Priscila de Aquino                                                                ******)
5(******                                                                                                   ******)
6(****** Choose whether Feynman gauge is desired.                                                          ******)
7(****** If set to False, unitary gauge is assumed.                                                          ****)
8(****** Feynman gauge is especially useful for CalcHEP/CompHEP where the calculation is 10-100 times faster. ***)
9(****** Feynman gauge is not supported in MadGraph and Sherpa.                                              ****)
10(***************************************************************************************************************)
11
12M$ModelName = "LED";
13
14M$Information = {Authors -> {"Priscila de Aquino"},
15             Date -> "15.06.2009",
16             Institute -> {"Katholieke Universiteit Leuven & Universite Catholique Louvain - CP3"},
17             Emails -> {"priscila@itf.kuleuven.be"},
18             References -> {"Phys. Rev. D59: 105006 (1999), hep-ph/9811350", "Nucl. Phys. B544 (1999), hep-ph/9811291", "Eur. Phys. J. C56 (2008), hep-ph/0805.2554"},
19             URLs -> "http://feynrules.phys.ucl.ac.be/view/Main/LED",
20             Version -> "1.0"};
21
22FeynmanGauge = False;
23
24
25(*****************************************************************************************)
26(****************************** Index definitions ****************************************)
27(*****************************************************************************************)
28
29IndexRange[ Index[Generation] ] = Range[3]
30
31IndexRange[ Index[Colour] ] = NoUnfold[Range[3]]
32
33IndexRange[ Index[Gluon] ] = NoUnfold[Range[8]]
34
35IndexRange[ Index[SU2W] ] = Range[3]
36
37
38IndexStyle[Colour, i]
39
40IndexStyle[Generation, f]
41
42IndexStyle[Gluon ,a]
43
44IndexStyle[SU2W ,k]
45
46(*****************************************************************************************)
47(*************************************  Parameters ***************************************)
48(*****************************************************************************************)
49
50M$Parameters = {
51
52  (* External parameters *)
53
54  \[Alpha]EWM1== {
55        ParameterType -> External,
56        BlockName -> SMINPUTS,
57        ParameterName -> aEWM1,
58        InteractionOrder -> {QED, -2},
59        Value -> 127.9,
60        Description -> "Inverse of the electroweak coupling constant"},
61
62  Gf == {
63        ParameterType -> External,
64        BlockName -> SMINPUTS,
65        InteractionOrder -> {QED, 2},
66        Value -> 1.16639 * 10^(-5),
67        Description -> "Fermi constant"},
68
69  \[Alpha]S == {
70        ParameterType -> External,
71        BlockName -> SMINPUTS,
72        ParameterName -> aS,
73        InteractionOrder -> {QCD, 2},
74        Value -> 0.118,
75        Description -> "Strong coupling constant at the Z pole."},
76
77
78  ZM == {
79        ParameterType -> External,
80        BlockName -> SMINPUTS,
81        Value -> 91.188,
82        Description -> "Z mass"},
83
84
85  ymc == {
86        ParameterType -> External,
87        BlockName -> YUKAWA,
88        Value -> 1.42,
89        OrderBlock -> {4},
90        Description -> "Charm Yukawa mass"},
91
92 ymb == {
93        ParameterType -> External,
94        BlockName -> YUKAWA,
95        Value -> 4.7,
96        OrderBlock -> {5},
97        Description -> "Bottom Yukawa mass"},
98
99  ymt == {
100        ParameterType -> External,
101        BlockName -> YUKAWA,
102        Value -> 174.3,
103        OrderBlock -> {6},
104        Description -> "Top Yukawa mass"},
105
106  ymtau == {
107        ParameterType -> External,
108        BlockName -> YUKAWA,
109        Value -> 1.777,
110        OrderBlock -> {15},
111        Description -> "Tau Yukawa mass"},
112
113   GN == {
114        ParameterType -> External,
115        ParameterName -> GN,
116        InteractionOrder -> {QCD, 2},
117        Value -> 10^(-16),
118        Description -> "Newton Constant"},
119
120   (* Internal Parameters *)
121
122  \[Alpha]EW == {
123        ParameterType -> Internal,
124        Value -> 1/\[Alpha]EWM1,
125        ParameterName -> aEW,
126        InteractionOrder -> {QED, 2},
127        Description -> "Electroweak coupling contant"},
128
129
130  MW == {
131        ParameterType -> Internal,
132        Value -> Sqrt[MZ^2/2+Sqrt[MZ^4/4-Pi/Sqrt[2]*\[Alpha]EW/Gf*MZ^2]],
133        Description -> "W mass"},
134
135  sw2 == {
136        ParameterType -> Internal,
137        Value -> 1-(MW/MZ)^2,
138        Description -> "Squared Sin of the Weinberg angle"},
139
140   ee == {
141        TeX -> e,
142        ParameterType -> Internal,
143        Value -> Sqrt[4 Pi \[Alpha]EW],
144        InteractionOrder -> {QED, 1},
145        Description -> "Electric coupling constant"},
146
147   cw == {
148        TeX -> Subscript[c, w],
149        ParameterType -> Internal,
150        Value -> Sqrt[1 - sw2],
151        Description -> "Cos of the Weinberg angle"}, 
152
153   sw == {
154        TeX -> Subscript[s, w],
155        ParameterType -> Internal,
156        Value -> Sqrt[sw2],
157        Description -> "Sin of the Weinberg angle"}, 
158
159   gw == {
160        TeX -> Subscript[g, w],
161        ParameterType -> Internal,
162        Value -> ee / sw,
163        InteractionOrder -> {QED, 1},
164        Description -> "Weak coupling constant"},
165
166   g1 == {
167        TeX -> Subscript[g, 1],
168        ParameterType -> Internal,
169        Value -> ee / cw,
170        InteractionOrder -> {QED, 1},
171        Description -> "U(1)Y coupling constant"},
172
173   gs == {
174        TeX -> Subscript[g, s],
175        ParameterType -> Internal,
176        Value -> Sqrt[4 Pi \[Alpha]S],
177        InteractionOrder -> {QCD, 1},
178        ParameterName -> G,
179        Description -> "Strong coupling constant"},
180
181   v == {
182        ParameterType -> Internal,
183        Value -> 2*MW*sw/ee,
184        InteractionOrder -> {QED, -1},
185        Description -> "Higgs VEV"},
186
187   \[Lambda] == {
188        ParameterType -> Internal,
189        Value -> MH^2/(2*v^2),
190        InteractionOrder -> {QED, 2},
191        ParameterName -> lam,
192        Description -> "Higgs quartic coupling"},
193
194   muH == {
195        ParameterType -> Internal,
196        Value -> Sqrt[v^2 \[Lambda]],
197        TeX -> \[Mu],
198        Description -> "Coefficient of the quadratic piece of the Higgs potential"},
199
200
201   yl == {
202        Indices -> {Index[Generation]},
203        AllowSummation -> True,
204        ParameterType -> Internal,
205        Value -> {yl[1] -> 0, yl[2] -> 0, yl[3] -> Sqrt[2] ymtau / v},
206        ParameterName -> {yl[1] -> ye, yl[2] -> ym, yl[3] -> ytau},
207        InteractionOrder -> {QED, 1},
208        ComplexParameter -> False,
209        Description -> "Lepton Yukawa coupling"},
210
211   yu == {
212        Indices -> {Index[Generation]},
213        AllowSummation -> True,
214        ParameterType -> Internal,
215        Value -> {yu[1] -> 0, yu[2] -> Sqrt[2] ymc / v, yu[3] -> Sqrt[2] ymt / v},
216        ParameterName -> {yu[1] -> yu, yu[2] -> yc, yu[3] -> yt},
217        InteractionOrder -> {QED, 1},
218        ComplexParameter -> False,
219        Description -> "U-quark Yukawa coupling"},
220
221   yd == {
222        Indices -> {Index[Generation]},
223        AllowSummation -> True,
224        ParameterType -> Internal,
225        Value -> {yd[1] -> 0, yd[2] -> 0, yd[3] -> Sqrt[2] ymb / v},
226        ParameterName -> {yd[1] -> yd, yd[2] -> ys, yd[3] -> yb},
227        InteractionOrder -> {QED, 1},
228        ComplexParameter -> False,
229        Description -> "D-quark Yukawa coupling"},
230
231   cabi == {
232        TeX -> Subscript[\[Theta], c],
233        ParameterType -> External,
234        BlockName -> CKMBLOCK,
235        OrderBlock -> {1},
236        Value -> 0.488,
237        Description -> "Cabibbo angle"},
238
239  CKM == {
240       Indices -> {Index[Generation], Index[Generation]},
241       TensorClass -> CKM,
242       Unitary -> True,
243       Value -> {CKM[1,2] -> Sin[cabi],
244                   CKM[1,1] -> Cos[cabi],
245                   CKM[2,1] -> -Sin[cabi],
246                   CKM[2,2] -> Cos[cabi]},
247       Description -> "CKM-Matrix"},
248
249   kappa == {
250        TeX -> \[Kappa],
251        ParameterType -> Internal,
252        Value -> Sqrt[16 Pi GN]}
253
254}
255
256TeXFormat[mphi, Subscript[m, phi]]
257TeXFormat[mpsi, Subscript[m, psi]]
258TeXFormat[mG, Subscript[m, G]]
259
260(*****************************************************************************************)
261(********************************* Gauge Groups ******************************************)
262(*****************************************************************************************)
263
264M$GaugeGroups = {
265
266  U1Y == {
267        Abelian -> True,
268        GaugeBoson -> B,
269        Charge -> Y,
270        CouplingConstant -> g1},
271
272  SU2L == {
273        Abelian -> False,
274        GaugeBoson -> Wi,
275        StructureConstant -> Eps,
276        CouplingConstant -> gw},
277
278  SU3C == {
279        Abelian -> False,
280        GaugeBoson -> G,
281        StructureConstant -> f,
282        SymmetricTensor -> dSUN,
283        Representations -> {T, Colour},
284        CouplingConstant -> gs}
285}
286(*****************************************************************************************)
287(******************************* Particle Classes ****************************************)
288(*****************************************************************************************)
289
290M$ClassesDescription = {
291
292(************************************ Fermions *******************************************)
293
294        (* Leptons (neutrino): I_3 = +1/2, Q = 0 *)
295  F[1] == {
296        ClassName -> vl,
297        ClassMembers -> {ve,vm,vt},
298        FlavorIndex -> Generation,
299        SelfConjugate -> False,
300        Indices -> {Index[Generation]},
301        Mass -> 0,
302        Width -> 0,
303        QuantumNumbers -> {LeptonNumber -> 1},
304        PropagatorLabel -> {"v", "ve", "vm", "vt"} ,
305        PropagatorType -> S,
306        PropagatorArrow -> Forward,
307        PDG -> {12,14,16},
308        FullName -> {"Electron-neutrino", "Mu-neutrino", "Tau-neutrino"} },
309
310        (* Leptons (electron): I_3 = -1/2, Q = -1 *)
311  F[2] == {
312        ClassName -> l,
313        ClassMembers -> {e, m, tt},
314        FlavorIndex -> Generation,
315        SelfConjugate -> False,
316        Indices -> {Index[Generation]},
317        Mass -> {Ml, {ME, 0}, {MM, 0}, {MTA, 1.777}},
318        Width -> 0,
319        QuantumNumbers -> {Q -> -1, LeptonNumber -> 1},
320        PropagatorLabel -> {"l", "e", "m", "tt"},
321        PropagatorType -> Straight,
322        ParticleName -> {"e-", "m-", "tt-"},
323        AntiParticleName -> {"e+", "m+", "tt+"},
324        PropagatorArrow -> Forward,
325        PDG -> {11, 13, 15},
326        FullName -> {"Electron", "Muon", "Tau"} },
327
328        (* Quarks (u): I_3 = +1/2, Q = +2/3 *)
329  F[3] == {
330        ClassMembers -> {u, c, t},
331        ClassName -> uq,
332        FlavorIndex -> Generation,
333        SelfConjugate -> False,
334        Indices -> {Index[Generation], Index[Colour]},
335        Mass -> {Mu, {MU, 0}, {MC, 1.42}, {MT, 174.3}},
336        Width -> {0, 0, {WT, 1.50833649}},
337        QuantumNumbers -> {Q -> 2/3},
338        PropagatorLabel -> {"uq", "u", "c", "t"},
339        PropagatorType -> Straight,
340        PropagatorArrow -> Forward,
341        PDG -> {2, 4, 6},
342        FullName -> {"u-quark", "c-quark", "t-quark"}},
343
344        (* Quarks (d): I_3 = -1/2, Q = -1/3 *)
345  F[4] == {
346        ClassMembers -> {d, s, b},
347        ClassName -> dq,
348        FlavorIndex -> Generation,
349        SelfConjugate -> False,
350        Indices -> {Index[Generation], Index[Colour]},
351        Mass -> {Md, {MD, 0}, {MS, 0}, {MB, 4.7}},
352        Width -> 0,
353        QuantumNumbers -> {Q -> -1/3},
354        PropagatorLabel -> {"dq", "d", "s", "b"},
355        PropagatorType -> Straight,
356        PropagatorArrow -> Forward,
357        PDG -> {1,3,5},
358        FullName -> {"d-quark", "s-quark", "b-quark"} },
359
360(************************************ Gauge Bosons ***************************************)
361
362        (* Gauge bosons: Q = 0 *)
363  V[1] == {
364        ClassName -> A,
365        SelfConjugate -> True,
366        Indices -> {},
367        Mass -> 0,
368        Width -> 0,
369        PropagatorLabel -> "a",
370        PropagatorType -> W,
371        PropagatorArrow -> None,
372        PDG -> 22,
373        FullName -> "Photon" },
374
375  V[2] == {
376        ClassName -> Z,
377        SelfConjugate -> True,
378        Indices -> {},
379        Mass -> {MZ, 91.188},
380        Width -> {WZ, 2.44140351},
381        PropagatorLabel -> "Z",
382        PropagatorType -> Sine,
383        PropagatorArrow -> None,
384        PDG -> 23,
385        FullName -> "Z" },
386
387        (* Gauge bosons: Q = -1 *)
388  V[3] == {
389        ClassName -> W,
390        SelfConjugate -> False,
391        Indices -> {},
392        Mass -> {MW, Internal},
393        Width -> {WW, 2.04759951},
394        QuantumNumbers -> {Q -> 1},
395        PropagatorLabel -> "W",
396        PropagatorType -> Sine,
397        PropagatorArrow -> Forward,
398        ParticleName ->"W+",
399        AntiParticleName ->"W-",
400        PDG -> 24,
401        FullName -> "W" },
402
403V[4] == {
404        ClassName -> G,
405        SelfConjugate -> True,
406        Indices -> {Index[Gluon]},
407        Mass -> {mG,0},
408        Width -> 0,
409        PropagatorLabel -> G,
410        PropagatorType -> C,
411        PropagatorArrow -> None,
412        PDG -> 21,
413        FullName -> "G" },
414
415V[5] == {
416        ClassName -> Wi,
417        Unphysical -> True,
418        Definitions -> {Wi[mu_, 1] -> (W[mu] + Wbar[mu])/Sqrt[2],
419                        Wi[mu_, 2] -> (Wbar[mu] - W[mu])/Sqrt[2]/I,
420                        Wi[mu_, 3] -> cw Z[mu] + sw A[mu]},
421        SelfConjugate -> True,
422        Indices -> {Index[SU2W]},
423        FlavorIndex -> SU2W,
424        Mass -> 0,
425        PDG -> {1,2,3}},
426
427V[6] == {
428        ClassName -> B,
429        SelfConjugate -> True,
430        Definitions -> {B[mu_] -> -sw Z[mu] + cw A[mu]},
431        Indices -> {},
432        Mass -> 0,
433        Unphysical -> True},
434
435(****************************** Scalar Fields *********************************************)
436       
437(* physical Higgs: Q = 0 *)
438  S[1] == {
439        ClassName -> H,
440        SelfConjugate -> True,
441        Mass -> {MH, 120},
442        Width -> {WH, 0.00575308848},
443        PropagatorLabel -> "H",
444        PropagatorType -> D,
445        PropagatorArrow -> None,
446        PDG -> 25,
447        TeXParticleName -> "\\phi",
448        TeXClassName -> "\\phi",
449        FullName -> "H" },
450
451S[2] == {
452        ClassName -> phi,
453        SelfConjugate -> True,
454        Mass -> {MZ, 91.188},
455        Width -> Wphi,
456        PropagatorLabel -> "Phi",
457        PropagatorType -> D,
458        PropagatorArrow -> None,
459        ParticleName ->"phi0",
460        PDG -> 250,
461        FullName -> "Phi",
462        Goldstone -> Z },
463
464S[3] == {
465        ClassName -> phi2,
466        SelfConjugate -> False,
467        Mass -> {MW, Internal},
468        Width -> Wphi2,
469        PropagatorLabel -> "Phi2",
470        PropagatorType -> D,
471        PropagatorArrow -> None,
472        ParticleName ->"phi+",
473        AntiParticleName ->"phi-",
474        PDG -> 251,
475        FullName -> "Phi2",
476        TeXClassName -> "\\phi^+",
477        TeXParticleName -> "\\phi^+",
478        TeXAntiParticleName -> "\\phi^-",
479        Goldstone -> W,
480        QuantumNumbers -> {Q -> 1}},
481
482(******************************* Spin 2 particles: graviton *****************************)
483
484T[1] == {
485     ClassName -> h,
486     SelfConjugate -> True,
487     Symmetric -> True,
488     Mass -> {Mh, 500}}
489
490}
491
492(*****************************************************************************************)
493(*                                                                                       *)
494(*                                   The Lagrangian                                      *)
495(*                                                                                       *)
496(*****************************************************************************************)
497
498(* Some shorthands (for nicer printing) *)
499
500Format[mu, TraditionalForm] = \[Mu];
501Format[nu, TraditionalForm] = \[Nu];
502Format[lam, TraditionalForm] = \[Lambda];
503Format[rho, TraditionalForm] = \[Rho];
504
505psi = \[Psi];
506psibar = \[Psi]bar;
507phi = \[Phi];
508phibar = \[Phi]bar;
509phiK = \[Sigma];
510
511(*****************************************************************************************)
512(********************** Defining the cov derivatives ************************************)
513(*****************************************************************************************)
514
515covdelU[field_, mu_] :=
516  Module[{j, a},   del[field, mu] - I gs G[mu, a] T[a].field
517                 - I ee/cw 4/3 B[mu]/2 ProjP.field - I ee/cw/3 B[mu]/2 ProjM.field - I ee/sw/2 ProjM.field Wi[mu,3]];
518
519covdelD[field_, mu_] :=
520  Module[{j, a}, del[field, mu] - I gs G[mu, a] T[a].field
521                 + I ee/cw 2/3 B[mu]/2 ProjP.field - I ee/cw/3 B[mu]/2 ProjM.field + I ee/sw/2 ProjM.field Wi[mu,3]];
522
523covdelE[field_, mu_] :=
524  Module[{j, a},  del[field, mu]
525                 + I 2 ee/cw B[mu]/2 ProjP.field - I ee/cw B[mu]/2 ProjM.field + I ee/sw/2 ProjM.field Wi[mu,3]];
526
527covdelN[field_, mu_] :=
528  Module[{j, a}, del[field, mu] + I ee/cw B[mu]/2 ProjM.field - I ee/sw/2 ProjM. field Wi[mu,3]];
529
530(*****************************************************************************************)
531(******************** Defining the field strenght tensors:********************************)
532(*****************************************************************************************)
533
534FG[mu_,nu_,a1_,a2_,a3_] := del[G[nu, a1], mu] - del[G[mu, a1], nu] + gs f[a1, a2, a3] G[mu, a2] G[nu, a3];
535
536FA[mu_,nu_] := del[B[nu], mu] - del[B[mu], nu];
537
538FW[mu_,nu_,i1_,i2_,i3_] := del[Wi[nu, i1], mu] - del[Wi[mu, i1], nu] + ee/sw Eps[i1, i2, i3] Wi[mu, i2] Wi[nu, i3];
539
540
541
542(*****************************************************************************************)
543(******************* Defining the energy-momentum tensor T[mu,nu] ************************)
544(*****************************************************************************************)
545
546(* Gauge bosons *)
547
548TG[mu_,nu_]:= ( -ME[mu,nu]. (-1/4 FA[rho, sig] FA[rho,sig] - 1/4 FW[rho,sig,i1,i2,i3] FW[rho,sig, i1,i4,i5] - 1/4 FG[rho,sig,a1,a2,a3] FG[rho,sig, a1,a4,a5])
549                -FA[mu,rho] FA[nu,rho] - FW[mu,rho,i1,i2,i3] FW[nu,rho, i1,i4,i5] - FG[mu,rho,a1,a2,a3] FG[nu,rho, a1,a2,a3]);
550
551(* Fermions *)
552
553TF[mu_,nu_] := (-ME[mu,nu].(I uqbar.(Ga[rho].covdelU[uq, rho]) -1/2 del[I uqbar.Ga[rho].uq, rho]
554                          + I dqbar.(Ga[rho].covdelD[dq, rho]) -1/2 del[I dqbar.Ga[rho].dq, rho]
555                          + I vlbar.(Ga[rho].covdelN[vl, rho]) -1/2 del[I vlbar.Ga[rho].vl, rho]
556                          + I lbar.(Ga[rho].covdelE[l, rho]  ) -1/2 del[I lbar.Ga[rho].l, rho]
557                         
558                          - ee/sw/2 Sqrt[2] (CKM uqbar.Ga[rho].ProjM.dq W[rho] + HC[CKM] dqbar.Ga[rho].ProjM.uq Wbar[rho]
559                                         + vlbar.Ga[rho].ProjM.l W[rho] + lbar.Ga[rho].ProjM.vl Wbar[rho]) )
560               + (    I/2  uqbar.Ga[mu].covdelU[uq, nu] - 1/4 I del[uqbar.Ga[nu].uq, mu]
561                    + I/2  uqbar.Ga[nu].covdelU[uq, mu] - 1/4 I del[uqbar.Ga[mu].uq, nu]                   
562                    + I/2  dqbar.Ga[mu].covdelD[dq, nu] - 1/4 I del[dqbar.Ga[nu].dq, mu]
563                    + I/2  dqbar.Ga[nu].covdelD[dq, mu] - 1/4 I del[dqbar.Ga[mu].dq, nu]
564                    + I/2  vlbar.Ga[mu].covdelN[vl, nu] - 1/4 I del[vlbar.Ga[nu].vl, mu]
565                    + I/2  vlbar.Ga[nu].covdelN[vl, mu] - 1/4 I del[vlbar.Ga[mu].vl, nu]                   
566                    + I/2  lbar.Ga[mu].covdelE[l, nu] - 1/4 I del[lbar.Ga[nu].l, mu]
567                    + I/2  lbar.Ga[nu].covdelE[l, mu] - 1/4 I del[lbar.Ga[mu].l, nu]  )
568
569                - ee/sw/Sqrt[2] (  CKM uqbar.Ga[mu].ProjM.dq W[nu] + HC[CKM] dqbar.Ga[mu].ProjM.uq Wbar[nu]
570                              + CKM uqbar.Ga[nu].ProjM.dq W[mu] + HC[CKM] dqbar.Ga[nu].ProjM.uq Wbar[mu]                               
571                              + vlbar.Ga[mu].ProjM.l W[nu] + lbar.Ga[mu].ProjM.vl Wbar[nu]
572                              + vlbar.Ga[nu].ProjM.l W[mu] + lbar.Ga[nu].ProjM.vl Wbar[mu]));
573
574(* Definitions for Higgs and Yukawa *)
575
576 Phi := If[FeynmanGauge, {-I phi2, (v + H + I phi)/Sqrt[2]}, {0, (v + H)/Sqrt[2]}];
577 Phibar := If[FeynmanGauge, {I phi2bar, (v + H - I phi)/Sqrt[2]} ,{0, (v + H)/Sqrt[2]}];
578 
579 PMVec = Table[PauliSigma[i], {i, 3}];   
580 Wvec[mu_] := {Wi[mu, 1], Wi[mu, 2], Wi[mu, 3]};
581
582 Dc[f_, mu_] := I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 (Wvec[mu].PMVec).f;
583 Dcbar[f_, mu_] := -I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 f.(Wvec[mu].PMVec);
584 
585 Vphi[Phi_, Phibar_] := -muH^2 Phibar.Phi + \[Lambda] (Phibar.Phi)^2;
586
587
588(* Higgs *)
589
590TH[mu_, nu_] := (-ME[mu,nu].(Dcbar[Phibar, rho]).Dc[Phi, rho] - Vphi[Phi, Phibar]+
591    (Dcbar[Phibar, mu]).Dc[Phi, nu] + (Dcbar[Phibar, nu]).Dc[Phi, mu] );
592
593(* Yukawa *)
594
595TYuk:= Module[{s,r,n,m,i},                                                    -
596              yd[n]              dqbar[s,n,i].ProjP[s,r].dq[r,n,i] (v+H)/Sqrt[2]  -
597              yu[n]              uqbar[s,n,i].ProjP[s,r].uq[r,n,i] (v+H)/Sqrt[2]  -
598              yl[n]               lbar[s,n].ProjP[s,r].l[r,n]      (v+H)/Sqrt[2]];
599
600TY[mu_,nu_] := -ME[mu,nu].(TYuk + HC[TYuk]);
601
602
603(*****************************************************************************************)
604(*******************************  Writing the lagrangian *********************************)
605(*****************************************************************************************)
606
607LagH := -kappa/2 (h[mu,nu].TH[mu,nu]);
608
609LagG := -kappa/2 (h[mu,nu].TG[mu,nu]);
610
611LagF := -kappa/2 (h[mu,nu].TF[mu,nu]);
612
613LagY := -kappa/2 (h[mu,nu].TY[mu,nu])
614
615
616(*****************************************************************************************)
617